Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂×Dic₇

Direct product G=N×Q with N=C₂³ and Q=C₂×Dic₇

		d	ρ	Label	ID
C₂⁴×Dic₇		448		C2^4xDic7	448,1383

Semidirect products G=N:Q with N=C₂³ and Q=C₂×Dic₇

extension	φ:Q→Aut N	d	Label	ID
C₂³⋊₁(C₂×Dic₇) = C₂×C₂³⋊Dic₇	φ: C₂×Dic₇/C₁₄ → C₄ ⊆ Aut C₂³	112	C2^3:1(C2xDic7)	448,753
C₂³⋊₂(C₂×Dic₇) = C₂⁴.₁₈D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	224	C2^3:2(C2xDic7)	448,754
C₂³⋊₃(C₂×Dic₇) = C₂⁴.₃₈D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	112	C2^3:3(C2xDic7)	448,1251
C₂³⋊₄(C₂×Dic₇) = C₂×D₄×Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224	C2^3:4(C2xDic7)	448,1248
C₂³⋊₅(C₂×Dic₇) = C₂²×C₂³.D₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224	C2^3:5(C2xDic7)	448,1292

Non-split extensions G=N.Q with N=C₂³ and Q=C₂×Dic₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₂×Dic₇) = C₂⁴⋊Dic₇	φ: C₂×Dic₇/C₁₄ → C₄ ⊆ Aut C₂³	56	4	C2^3.1(C2xDic7)	448,93
C₂³.₂(C₂×Dic₇) = (C₂²×C₂₈)⋊C₄	φ: C₂×Dic₇/C₁₄ → C₄ ⊆ Aut C₂³	112	4	C2^3.2(C2xDic7)	448,96
C₂³.₃(C₂×Dic₇) = (D₄×C₁₄).₁₆C₄	φ: C₂×Dic₇/C₁₄ → C₄ ⊆ Aut C₂³	112	4	C2^3.3(C2xDic7)	448,771
C₂³.₄(C₂×Dic₇) = (D₄×C₁₄)⋊₁₀C₄	φ: C₂×Dic₇/C₁₄ → C₄ ⊆ Aut C₂³	112	4	C2^3.4(C2xDic7)	448,774
C₂³.₅(C₂×Dic₇) = C₂⁴.₂D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	112		C2^3.5(C2xDic7)	448,84
C₂³.₆(C₂×Dic₇) = (C₂×C₂₈).Q₈	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	112	4	C2^3.6(C2xDic7)	448,90
C₂³.₇(C₂×Dic₇) = C₂⁴.₈D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.7(C2xDic7)	448,485
C₂³.₈(C₂×Dic₇) = C₄².₁₈₇D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.8(C2xDic7)	448,534
C₂³.₉(C₂×Dic₇) = C₂₈⋊₃M₄(2)	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.9(C2xDic7)	448,546
C₂³.₁₀(C₂×Dic₇) = C₂⁴.₁₉D₁₄	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	224		C2^3.10(C2xDic7)	448,755
C₂³.₁₁(C₂×Dic₇) = C₂₈.₇₆C₂⁴	φ: C₂×Dic₇/C₁₄ → C₂² ⊆ Aut C₂³	112	4	C2^3.11(C2xDic7)	448,1272
C₂³.₁₂(C₂×Dic₇) = C₂²⋊C₄×Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.12(C2xDic7)	448,475
C₂³.₁₃(C₂×Dic₇) = C₂⁴.₄₇D₁₄	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.13(C2xDic7)	448,484
C₂³.₁₄(C₂×Dic₇) = C₂₈.₅C₄²	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.14(C2xDic7)	448,531
C₂³.₁₅(C₂×Dic₇) = C₄².₄₃D₁₄	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.15(C2xDic7)	448,533
C₂³.₁₆(C₂×Dic₇) = D₄×C₇⋊C₈	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.16(C2xDic7)	448,544
C₂³.₁₇(C₂×Dic₇) = C₄².₄₇D₁₄	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.17(C2xDic7)	448,545
C₂³.₁₈(C₂×Dic₇) = (D₄×C₁₄).₁₁C₄	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.18(C2xDic7)	448,768
C₂³.₁₉(C₂×Dic₇) = C₂×Q₈.Dic₇	φ: C₂×Dic₇/Dic₇ → C₂ ⊆ Aut C₂³	224		C2^3.19(C2xDic7)	448,1271
C₂³.₂₀(C₂×Dic₇) = C₂⁴.Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.20(C2xDic7)	448,82
C₂³.₂₁(C₂×Dic₇) = C₂⁴.D₁₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.21(C2xDic7)	448,83
C₂³.₂₂(C₂×Dic₇) = (C₂×C₂₈)⋊C₈	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.22(C2xDic7)	448,85
C₂³.₂₃(C₂×Dic₇) = C₂₈.(C₄⋊C₄)	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.23(C2xDic7)	448,87
C₂³.₂₄(C₂×Dic₇) = C₄×C₄.Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.24(C2xDic7)	448,456
C₂³.₂₅(C₂×Dic₇) = C₂₈⋊₇M₄(2)	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.25(C2xDic7)	448,458
C₂³.₂₆(C₂×Dic₇) = C₄².₆Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.26(C2xDic7)	448,459
C₂³.₂₇(C₂×Dic₇) = C₄².₇Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.27(C2xDic7)	448,460
C₂³.₂₈(C₂×Dic₇) = C₂⁴.₄Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.28(C2xDic7)	448,741
C₂³.₂₉(C₂×Dic₇) = C₄×C₂³.D₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.29(C2xDic7)	448,743
C₂³.₃₀(C₂×Dic₇) = C₂⁴.₆₃D₁₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.30(C2xDic7)	448,745
C₂³.₃₁(C₂×Dic₇) = C₂³.₂₇D₂₈	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.31(C2xDic7)	448,746
C₂³.₃₂(C₂×Dic₇) = C₂×C₂₈.D₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.32(C2xDic7)	448,750
C₂³.₃₃(C₂×Dic₇) = C₂×C₂₈.₁₀D₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.33(C2xDic7)	448,760
C₂³.₃₄(C₂×Dic₇) = C₂⁵.D₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	112		C2^3.34(C2xDic7)	448,781
C₂³.₃₅(C₂×Dic₇) = C₂²×C₄.Dic₇	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.35(C2xDic7)	448,1234
C₂³.₃₆(C₂×Dic₇) = C₂×C₂³.₂₁D₁₄	φ: C₂×Dic₇/C₂×C₁₄ → C₂ ⊆ Aut C₂³	224		C2^3.36(C2xDic7)	448,1239
C₂³.₃₇(C₂×Dic₇) = (C₂×C₂₈)⋊₃C₈	central extension (φ=1)	448		C2^3.37(C2xDic7)	448,81
C₂³.₃₈(C₂×Dic₇) = C₂×C₄×C₇⋊C₈	central extension (φ=1)	448		C2^3.38(C2xDic7)	448,454
C₂³.₃₉(C₂×Dic₇) = C₂×C₄².D₇	central extension (φ=1)	448		C2^3.39(C2xDic7)	448,455
C₂³.₄₀(C₂×Dic₇) = C₂×C₂₈⋊C₈	central extension (φ=1)	448		C2^3.40(C2xDic7)	448,457
C₂³.₄₁(C₂×Dic₇) = C₂×C₂₈.₅₅D₄	central extension (φ=1)	224		C2^3.41(C2xDic7)	448,740
C₂³.₄₂(C₂×Dic₇) = C₂×C₁₄.C₄²	central extension (φ=1)	448		C2^3.42(C2xDic7)	448,742
C₂³.₄₃(C₂×Dic₇) = C₂³×C₇⋊C₈	central extension (φ=1)	448		C2^3.43(C2xDic7)	448,1233
C₂³.₄₄(C₂×Dic₇) = C₂²×C₄×Dic₇	central extension (φ=1)	448		C2^3.44(C2xDic7)	448,1235
C₂³.₄₅(C₂×Dic₇) = C₂²×C₄⋊Dic₇	central extension (φ=1)	448		C2^3.45(C2xDic7)	448,1238

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Extensions 1→N→G→Q→1 with N=C23 and Q=C2×Dic7

Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂×Dic₇